To find the length between the points \((2, 5)\) and \((7, 3)\), we can use the distance formula, which is derived from the Pythagorean Theorem:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (2, 5)\) and \((x_2, y_2) = (7, 3)\). Now, let's plug in the values:
\[ d = \sqrt{(7 - 2)^2 + (3 - 5)^2} \]
Calculating inside the parentheses:
\[ d = \sqrt{(5)^2 + (-2)^2} \]
Calculating the squares:
\[ d = \sqrt{25 + 4} \]
Adding them together:
\[ d = \sqrt{29} \]
Now, calculate \(\sqrt{29}\):
\[ \sqrt{29} \approx 5.385 \]
Rounding to the nearest hundredth gives:
\[ 5.39 \]
So, the length between the points \((2, 5)\) and \((7, 3)\) is approximately 5.39.